Remark 3 
Notice that the derived maximization problems (REF ) share similarities with the algorithm proposed in [1]} to solve value iteration over discrete-action IMDPs. In both cases, given a specific action \(a\) , a combination of additions of lower and upper bounds on transition probabilities is found, which is optimal w.r.t. the ordered value-function vector. The number of possible such combinations is \(|\mathcal {Q}|\)  in both cases. Nevertheless, contrary to here, in [1]} there is a stopping criterion, based on which the algorithm may terminate before computing all \(|\mathcal {Q}|\)  combinations. The existence of such a stopping criterion for problems (REF ) (i.e., for the continuous-action case) is an open question, and a potential affirmative answer would significantly reduce computations.

